Ray shooting and other applications of spanning trees with low stabbing number
SIAM Journal on Computing
Intersection number of two connected geometric graphs
Information Processing Letters
Planar minimally rigid graphs and pseudo-triangulations
Proceedings of the nineteenth annual symposium on Computational geometry
Pseudotriangulations from Surfaces and a Novel Type of Edge Flip
SIAM Journal on Computing
On plane spanning trees and cycles of multicolored point sets with few intersections
Information Processing Letters
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We study the following Ramsey-type problem. Let S=B@?R be a two-colored set of n points in the plane. We show how to construct, in O(nlogn) time, a crossing-free spanning tree T(B) for B, and a crossing-free spanning tree T(R) for R, such that both the number of crossings between T(B) and T(R) and the diameters of T(B) and T(R) are kept small. The algorithm is conceptually simple and is implementable without using any non-trivial data structure. This improves over a previous method in Tokunaga [Intersection number of two connected geometric graphs, Inform. Process. Lett. 59 (1996) 331-333] that is less efficient in implementation and does not guarantee a diameter bound. Implicit to our approach is a new proof for the result in the reference above on the minimum number of crossings between T(B) and T(R).